Analysis of dispersed, conducting-system frequency-response data

Widely used equations for the analysis of dispersive relaxation data for conducting materials, developed by Moynihan and associates more than two decades ago, are shown to be require correction. Corrected equations which can differ appreciably in their consequences from those of Moynihan et al. are derived and used to justify the empirical Barton, Nakajima, Namikawa (BNN) formula satisfied by much frequency-response data for disordered materials. The conductive-system frequency-response analysis described in the paper and the corrected Moynihan approach both allow arbitrary fitting models to be used. It is shown that, for one class of models, the two fitting approaches are identical and yield maximum information while, for other models, the fit information is intrinsically more limited and inaccurate. Improved methods for inverting transient-response data to yield the associated distribution of relaxation times and frequency response are compared with the approach Moynihan et al. used for the fractional-exponential fitting model (KWW), and a misconception in their work is corrected. Correct and incorrect ways to invert frequency-response data that include the effects of a high-frequency-limiting dielectric constant are illustrated for KWW response. The conventional KWW model yields physically unrealizable time and frequency responses, but a modification which restores realizability is developed. Analysis approaches are described which allow one to identify the type of dispersed behavior present in the data: either conductive- or dielectric-system response. Weighted, complex-non-linear-least-squares analyses of frequency-response data for Li2O-Al2O3-2SiO(2) glass at 24 degrees C using an approximate KWW fitting model are compared with earlier fitting results of the same data obtained by Moynihan and others using the Moynihan et al. equations and fitting approach. Excellent fits were obtained over the entire measured frequency range when the fitting model included elements accounting for electrode polarization effects in the data. These effects are shown to make non-negligible contributions at both extremes of the frequency-response range. Such contributions, and the past use of the Moynihan approach, probably explain most previously unexplained excess losses found present in the high frequency region, ones which Moynihan and associates characterized as endemic to the vitreous state.